=Paper=
{{Paper
|id=Vol-1664/w9
|storemode=property
|title=A Bayesian Computational Model for Trust on Information Sources
|pdfUrl=https://ceur-ws.org/Vol-1664/w9.pdf
|volume=Vol-1664
|authors=Alessandro Sapienza,Rino Falcone
|dblpUrl=https://dblp.org/rec/conf/woa/SapienzaF16
}}
==A Bayesian Computational Model for Trust on Information Sources==
https://ceur-ws.org/Vol-1664/w9.pdf
A Bayesian Computational Model for
Trust on Information Sources
Alessandro Sapienza and Rino Falcone
Institute of Cognitive Sciences and Technologies, ISTC – CNR,
Rome, Italy
{alessandro.sapienza, rino.falcone}@istc.cnr.it
Abstract— In this work we want to provide a tool for handling willingness (intentions, persistence, reliability, honesty,
information coming from different information sources. In fact sincerity, etc.).
the real world we often have to deal with different sources Moreover this form of trust is not empty, but it possesses a
asserting different things and, in order to decide, it is necessary more or less specified argument: the trustor X can not just
to consider properly each of them trying to put this information
trust Y, as trust is for/about something, it has a specific object:
together. According to us, a good way to do it is exploiting the
concept of trust. In fact using it as a valve, it is possible to give a what X expects from Y; Y’s service, action, provided well.
different weight to what the source is reporting. Plus we decide to And it is also context-dependent: in a given situation; with
implement this trust model as generic as possible. In this way, the internal or external causal attribution in case
model can be used in different context and within different
practical applications. Then, according to our view [3] trusting an information source
(S) means to use a cognitive model based on the dimensions of
After presenting the theoretical and the computational model, competence and motivation of the source. These competence
we also show a practical example of how to use it, to let the
and motivation evaluations can derive from different reasons,
reader better understand the overall workflow.
basically:
Keywords—trust; cognitive model; bayesian theory • Our previous direct experience with S on that
specific kind of information content.
I. INTRODUCTION • Recommendations (other individuals Z reporting their
In the world we often have to deal with different information direct experience and evaluation about S) or
coming from different information sources. Though having a Reputation (the shared general opinion of others
lot of sources can be very useful, on the other hand, trying to about S) on that specific information content
put together information coming from different information [5][11][15][16][19].
sources can be an uneasy task. It is necessary to have • Categorization of S (it is assumed that a source can
strategies to do it, especially in presence of critical situation, be categorized and that it is known this category),
when there are temporal limits to make decision and a wrong exploiting inference and reasoning (analogy,
choice can lead to an economical loss or even to risk life. inheritance, etc.): on this basis it is possible to
As said, the possibility of integrating sources on different establish the competence/reliability of S on that
scopes can be very useful in order to make a well-informed specific information content [1][2][7][8]. In past
decision. works, we showed that exploiting categories for trust
Integrating these sources becomes essential, but at the same evaluations can represent a significant advantage
time it is necessary to identify and take into account their [9][10].
trustworthiness.
Considering information’s output, it can be a true/false one
In our perspective [3][4] trust in information sources is just a (the source can just assert or deny the belief P) or there can be
kind of social trust, preserving all its prototypical properties multiple outcomes. As this is a general model, we suppose that
and dimensions; just adding new important features and there can be different outcomes. For instance, the weather is
dynamics. In particular, also the trust in information sources not just good or bad, but can assume multiple values (critical,
[6] can just be an evaluation, judgment and feeling, or be a sunny, cloudy etc.).
decision to rely on, and act of believing in and to the trustee
(Y) and rely on it. Also this trust and has two main
dimensions: the ascribed competence versus the ascribed
50
II. THE BAYESIAN CHOICE how much the specific information should be considered, with
There are many ways to computationally realize a decision respect to the global information.
making process and quite all of them provide good results.
Dealing with uncertain situations, one can use the uncertainty This process can be done in presence of a single or multiple
theory [12], a mathematical approach specifically created to sources, as each time we perform an aggregation of each
evaluate belief degree in cases in which there is no data. contribute to the global evidence.
Another possible way is to use fuzzy logic [17]. This A strong point of this model is that it is sequential, so it can be
technique has several vantages like: updated when new information comes.
1. It is flexible and easy to use;
2. It don’t need precise data; A. Source’s Evaluation
3. It can deal with non linear functions;
The first part of the model concerns the source’s evaluation.
4. It is able to shape human way of think and express, as
According to us, there are two level of evaluation. Initially, we
it can model concept that are more complex than a produce an a priori trust, which represent how much I believe
Boolean but not so precise like a real number. that S is good with this specific kind of information.
After that, we compute a more sophisticated analysis taking
Maybe the most used approach is the probabilistic one, which
into account other parameters.
exploits the Bayesian theory, in particular probability
distribution.
Let’s first start from the a priori source’s evaluation –
One of the advantages of using Bayesian theory is that it
𝑆𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛. This is the trustor’s trust about P just
implies a sequential process: every time that new evidence
occurs it can be processed individually and then aggregated to depending on the its judgment of the S’s competence and
global evidence. This property is really useful as it allows a willingness as derived from the composition of the three
trustor to elaborate its information in a moment and update it factors (direct experience, recommendation/reputation, and
whenever it gets other evidence. categorization), in practice the S’s credibility about P on view
of the trustor.
Given the context of information sources, we believe that this Recalling that a trust evaluation for a cognitive agent is based
last option is the choice that best suits with the problem. In on the two aspects of competence and willingness, we state
fact there is a fixed number of known possibilities to model that these values can be obtained using three different
and the trustor can collect information from its sources dimensions:
individually and then aggregate them in different moment.
Plus, the scientific literature confirms its utility in the context 1. Direct experience with S (how S performed in the
of trust evaluation[13][14][18]. past interactions) on that specific information
content;
2. Recommendations (other individuals Z reporting
III. THE COMPUTATIONAL MODEL their direct experience and evaluation about S) or
In the proposed model each information source S is Reputation (the shared general opinion of others
represented by a trust degree called 𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆, with 0≤ about S) on that specific information content;
𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆 ≤1, plus a bayesian probability distribution PDF 3. Categorization of S.
that represents the information reported by S.
The two faces of S’s trustworthiness (competence and
To the aim of granting a better flexibility, the PDF is modeled willingness) are relatively independent; however, for sake of
as a continuous distribution (actually it is divided into several simplicity, we will unify them into a unique quantitative
intervals and it is continuous in each interval). In fact if the parameter, by combining competence and reliability.
event domain is continuous it is better to use a continuous
PDF; if it happens to be discrete it is still possible to use a Computationally, the past experience (PE),
continuous PDF. It is also possible to specify what and how reputation/recommendation (REP) and categories (CAT)
much outcomes the model has to use, depending on the parameters are defined here as real values in the interval [0,1].
specific context. In the end of the paper we will show a To compute S’s evaluation we make a weighted mean of
working example in which we take into account five different them:
outcomes, then the PDF will be divided accordingly.
𝑆𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 = 𝑤1 ∗ 𝑃𝐸 + 𝑤2 ∗ 𝐶𝐴𝑇 + 𝑤3 ∗ 𝑅𝐸𝑃
The model we created starts from a preliminary evaluation of
the source trustworthiness: how much reliable is a source S The trustor, considering both its personality and the context in
concerning a specific information’s category? which it is, determines the weight w1, w2 and w3 empirically.
Then after evaluating it, we consider what the source is
reporting - the PDF. We use the trust evaluation to understand
51
B. Certainty and Identity
Computing the general trust on the Source concerning P is a
good starting point. However it is not enough. In fact, while
this value represents an a priori evaluation of how much a
source S is trustworthy, there are other two factors that can
influence a trust evaluation.
The first one is the S’s degree of certainty about P
(𝐶𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦). The information sources not only give the
information but also their certainty about this information. The
same information can be reported with different degree of
confidence (“I am sure about it”, “I suppose that”, “it is
possible that” and so on).
Of course we are interested in modeling this certainty, but we
have to consider that through the trustor’s point of view (it
subjectively estimates this parameter). It is defined as a real
value in range [0,1]. Figure 1: An example of a PDF
The second dimension represents the trustor’s degree of
trust that P derives from S (𝐼𝑑𝑒𝑛𝑡𝑖𝑡𝑦): the trust we have that It is not possible to consider the PDF as it is. The idea is that if
the information under analysis derives from that specific I think I am exploiting a reliable source, than it is good to take
source; it is defined as a real value in range [0,1]. This into account what it is saying. But if I suppose that the source
parameter has a twofold meaning: is unreliable, even if it is not competent or because there is a
1. For instance, considering the human communication I possibility it wants to deceive me, then I need to be cautious.
can be more or less sure that the specific information
under analysis has been reported by the source S. It is Here we propose an algorithm to deal with this problem,
a problem of memory, do I recall properly? combining the trust evaluation with what the source is
2. In the web context the communication’s dynamics reporting. In other words, we exploit the 𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆 value to
changes. I will probably receive the information by smooth the PDF. The output of this process is what we call the
someone hiding beyond a computer. How may I be Smoothed PDF (SPDF).
sure about it’s identity? Can I trust that S is really Recalling that the PDF is divided into segments, this is the
who is saying to be? This is a very complex issue and formula used for transforming each segments:
its solution has not been completely provided by 𝑆𝑒𝑔𝑚𝑒𝑛𝑡! = 1 + 𝑆𝑒𝑔𝑚𝑒𝑛𝑡! − 1 ∗ 𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆
computer scientist. If 𝑆𝑒𝑔𝑚𝑒𝑛𝑡! > 1 it will be lowered until 1. On the contrary, if
𝑆𝑒𝑔𝑚𝑒𝑛𝑡! < 1it will tend to increase to the value 1.
The source Evaluation is softened by the Certainty and the We will have that:
Identity parameters, since we considered them as two
multiplicative parameters. The output of this operation is the • The greater 𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆 is, the more similar the SPDF will
actual trust that the trustor has on S: be to the PDF; in particular if 𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆 =1 => SPDF
𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆 = 𝑆𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 ∗ 𝐼𝑑𝑒𝑛𝑡𝑖𝑡𝑦 ∗ 𝐶𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =PDF;
• The lesser it is, the more the SPDF will be flatten; in
particular if 𝑇𝑟𝑢𝑠𝑡𝑂𝑛𝑆 =0 => SPDF is an uniform
C. PDF: the reported information distribution with value 1.
With the PDF (Probability Distribution Function) we represent
the probability distribution that the source reports concerning The idea is that we trust on what S says proportionally to how
the belief P. much we trust S. In words, the more we trust S, the more we
Given a fixed number of outcomes, which depends on the tend to take into consideration what it says; the less we trust S,
nature of the information and on the accuracy of the source in the more we tend to ignore its informative contribution.
reporting the information, with the PDF a source S reports
how much it subjectively believes possible each single The picture 2 resumes the model until this point.
outcome.
Of course the source can assert that just one of them is
possible (100%) or it can divide the probability among them.
The picture 1 shows an example of what we mean with the
term PDF. It is divided in slots, each one representing a
possible outcome.
Figure 2: A scheme of the computational model until the
SPDF
52
The point is that considering uncertainty on information is
correct, but it is a too limitative approach. In fact uncertainty
D. The effect of each source/evidence on the Global PDF
comes up at different levels and has to be taken into account
We define GPDF (Global PDF) the evidence that an agent when deciding.
owns concerning a belief P. At the beginning, if the trustor Actually, in this model we handle it in three different ways.
does not possess any evidence about the belief P, the GPDF is
flat, as it is a uniform distribution. Otherwise it has a specific The first one is the uncertainty on the source. This is given
shape the models the specific internal belief of the trustor. by the source evaluation 𝑆𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛.
The second level is represented by uncertainty on
Each information source provides evidence about P, communication. This is handled by the two parameters
modifying then the GPDF owned by the trustor. Once Certainty and Identity: how much I’m sure about the identity
estimated the SPDFs for each information source, there will be of the source? How much certainty does the source express in
a process of aggregation between the GPDF and the SPDFs. reporting the information (according to the trustor)?
Each source actually represents a new evidence E about a The last level is the uncertainty on the reported information
belief P. Then to the purpose of the aggregation process it is (PDF). This is managed just by the intrinsic nature of the PDF.
possible to use the classical Bayesian logic, recursively on In fact what happens here is that the source express its
each source: certainty/uncertainty through the outcomes’ distributions.
𝑓 𝐸 𝑃 ∗𝑓 𝑃
𝑓 𝑃𝐸 =
𝑓 𝐸 In practice, we take into account uncertainty in all the process,
where: until the end, in order to produce a proper prediction.
f(P|E) = GPDF (the new one)
f(E|P) = SPDF;
f(P) = GPDF (the old one) IV. A WORKFLOW’S EXAMPLE
In this section we want to provide a working example of how
In this case f(E) is a normalization factor, given by the to use the model. As the trust computation is quite simple and
formula: intuitive, below we will directly use the TrustOnS parameter,
𝑓(𝐸) = 𝑓 𝐸 𝑃 ∗ 𝑓 𝑃 𝑑𝑃 together with the corresponding PDF.
Moreover, we will represent PDFs as a list of five values, with
In words the new GPDF, that is the global evidence that an the following formalism:
agent has about P, is computed as the product of the old GPDF 𝑃𝐹𝐷!" = [𝑥!! 𝑥!! 𝑥!! 𝑥!! 𝑥!! ]
and the SPDF, that is the new contribute reported by S. in which 𝑥!! 𝑥!! 𝑥!! 𝑥!! 𝑥!! 2 are the values of the PDF for the
As we need to ensure that GPDF is still a probability source Si in the corresponding segment.
distribution function, it is necessary to scale down it1. This is
ensured by the normalization factor f(E). Suppose that an agent has to understand what kind of weather
there will be the following day. It starts collecting forecast
The picture 3 represents the whole model for managing trust from its information sources. The possible outcomes are five:
on information sources {sunny day, cloudy day, light rain, heavy rain, critical rain}.
Let’s suppose that Source S1 has a TrustOnSS1=1 (the
maximal value) and that it is asserting PDFS1 = [0.5 0.5 0.5 3
0.5], so it mainly suppose that there will be heavy rain.
The visual representation of PDFS1 is provided by figure 4.
Figure 3: A scheme of the computational model until the
GPDF
Exploiting the GPDF, the trust is able to understand what is
the outcome Oi that is more likely to happen.
E. Handling uncertainty
Dealing with information, a critical point is how to handle
uncertainty.
2
Note that, from how the PDF has been defined, these parameters are
1
To be a PDF, it is necessary that the area subtended by it is equal to non-negative real numbers, with the peculiarity that their sum is
1. equal to 5.
53
Figure 4: The representation of PDFS1 in the example
Figure 6: The representation of GPDF in the example with the
contribute of S1 and S2.
As the trustor has the maximal trust on S1, PDFS1 and SPDFS1
will be the same. Plus, as this the first evidence on P, even the
As showed by figure 6, Thanks to the fact that the sources,
GPDF is equal to PDFS1.
even if with two different trust degrees, are asserting the same
things, there is a reinforcement of evidence in segment 4 of
Let then see what happens to S2, asserting the same of S1, but
the GPDF.
with a TrustOnSourceS2 of 0.7. The PDFS2 is the same of
This is a peculiarity that we shaped in our previous models
PDFS1, but the SPDFS2 is different, as showed by figure 5:
and that persist in this one as a consequence of the Bayes
theorem.
Let’s than see what happen in presence of a third source S3,
with TrustOsSourceS3 = 0.3 and PDFS3 = [0.3 3.8 0.3 0.3 0.3].
This source is reporting a cloudy day forecast. Its SPDF will
be:
The final result is showed by figure 7:
Figure 5: The representation of SPDFS2 in the example
The PDFS2 has been smoothed, so that values grater than 1 has
been decreased and values smaller than one has been
increased.
Let’s then see what happens to the GPDF:
Figure7: The final representation of GPDS in the example
The new GPDF is quite the same of the previous one. This is
due to the fact that, although S3 is strongly disagreeing with
S1 and S2, it has a low level of trust. Then it will lightly affect
what the trustor thinks.
In the end the trustor can assert that there will be heavy rain
the next day.
54
V. CONCLUSION [11] S. Jiang, J. Zhang, and Y.S. Ong. An evolutionary model for
constructing robust trust networks. In Proceedings of the 12th
The aim of this work was that of realizing a theoretical and International Conference on Autonomous Agents and Multiagent
computational model for dealing with information sources. Systems (AAMAS), 2013.
This is in fact an uneasy task and there can be critical [12] B. Liu, Uncertainty theory 5th Edition, Springer 2014.
situations in which agents have to face sources asserting [13] Melaye, D., & Demazeau, Y. (2005). Bayesian dynamic trust model. In
Multi-agent systems and applications IV (pp. 480-489). Springer Berlin
different things. Heidelberg.
We decided to realize a model as generic as possible. Doing [14] Quercia, D., Hailes, S., & Capra, L. (2006). B-trust: Bayesian trust
so, the model does not depend on a specific context and it can framework for pervasive computing. In Trust management (pp. 298-
be applied on different practical context. 312). Springer Berlin Heidelberg.
The basic idea is that using trust on information sources is a [15] Sabater-Mir, J. 2003. Trust and reputation for agent societies. Ph.D.
promising way to face the problem. Then, from a theoretical thesis, Universitat Autonoma de Barcelona
point of view, we analyzed all the possible cognitive variables [16] Sabater-Mir J., Sierra C., (2001), Regret: a reputation model for
gregarious societies. In 4th Workshop on Deception and Fraud in Agent
that can affect trust on an information source. Societies (pp. 61-70). Montreal, Canada.
After analyzing the various ways to represent information, we [17] Sapienza, A., Falcone, R., & Castelfranchi, C. Trust on Information
decided to exploit Bayesian theory. Then we showed how to Sources: A theoretical and computation approach, in proceedings of
apply the trust evaluation on the information layers in order to WOA 2014, ceur-ws, vol 1260, paper 12.
properly take into account information. [18] Wang, Y., & Vassileva, J. (2003, October). Bayesian network-based
Finally, we proposed a practical problem – the one of weather trust model. In Web Intelligence, 2003. WI 2003. Proceedings.
IEEE/WIC International Conference on (pp. 372-378). IEEE.
forecast – and we showed how to apply the model in order to
[19] Yolum, P. and Singh, M. P. 2003. Emergent properties of referral
get a solution. systems. In Proceedings of the 2nd International Joint Conference on
Autonomous Agents and MultiAgent Systems (AAMAS'03).
ACKNOWLEDGMENT
This work is partially supported by the project CLARA—
CLoud plAtform and smart underground imaging for natural
Risk Assessment, funded by the Italian Ministry of Education,
University and Research (MIUR-PON).
REFERENCES
[1] Burnett, C., Norman, T., and Sycara, K. 2010. Bootstrapping trust
evaluations through stereotypes. In Proceedings of the 9th International
Conference on Autonomous Agents and Multiagent Systems
(AAMAS'10). 241-248.
[2] Burnett, C., Norman, T., and Sycara, K. (2013) Stereotypical trust and
bias in dynamic multiagent systems. ACM Transactions on Intelligent
Systems and Technology (TIST), 4(2):26, 2013.
[3] Castelfranchi, C., Falcone R., Pezzulo, (2003) Trust in Information
Sources as a Source for Trust: A Fuzzy Approach, Proceedings of the
Second International Joint Conference on Autonomous Agents and
Multiagent Systems (AAMAS-03) Melburne (Australia), 14-18 July,
ACM Press, pp.89-96.
[4] Castelfranchi C., Falcone R., Trust Theory: A Socio-Cognitive and
Computational Model, John Wiley and Sons, April 2010.
[5] Conte R., and Paolucci M., 2002, Reputation in artificial societies.
Social beliefs for social order. Boston: Kluwer Academic Publishers
[6] Demolombe R., (1999), To trust information sources: A proposal for a
modal logic frame- work. In Castelfranchi C., Tan Y.H. (Eds), Trust and
Deception in Virtual Societies. Kluwer, Dordrecht.
[7] Falcone R, Castelfranchi C, (2008) Generalizing Trust: Inferencing
Trustworthiness from Categories. In Proceedings, pp. 65 - 80. R.
Falcone, S. K. Barber, J. Sabater-Mir, M. P. Singh (eds.). Lecture Notes
in Artificial Intelligence, vol. 5396. Springer, 2008
[8] Falcone R., Piunti, M., Venanzi, M., Castelfranchi C., (2013), From
Manifesta to Krypta: The Relevance of Categories for Trusting Others,
in R. Falcone and M. Singh (Eds.) Trust in Multiagent Systems, ACM
Transaction on Intelligent Systems and Technology, Volume 4 Issue 2,
March 2013
[9] Falcone, R., Sapienza, A., & Castelfranchi, C. (2015, July).
Recommendation of categories in an agents world: The role of (not)
local communicative environments. In Privacy, Security and Trust
(PST), 2015 13th Annual Conference on (pp. 7-13). IEEE.
[10] Falcone, R., Sapienza, A., & Castelfranchi, C. (2015). The relevance of
categories for trusting information sources. ACM Transactions on
Internet Technology (TOIT), 15(4), 13.
55